### Passive Delay Line Design Considerations - Rhombus

```Passive Delay Line
Design Considerations
Operating Specifications - Passive Delays
Pulse Overshoot (Pos) ............................................ 5% to 10%, typical
Pulse Distortion (S) ................................................................ 3% typical
Working Voltage .................................................... 25 VDC maximum
Dielectric Strength ................................................. 100VDC minimum
Insulation Resistance ................................ 1,000 MΩ min. @ 100VDC
Temperature Coefficient ..................................... 70 ppm/OC, typical
Bandwidth (fC) ............................................................... 0.35/tr approx.
Operating Temperature Range ................................... -55O to +125OC
Storage Temperature Range ........................................ -65O to +150OC
A Passive Delay Line is a special purpose Low Pass Filter
designed to delay (phase shift) the input signal by a specified
increment of time, and is composed of series inductors and
shunt capacitors with values dictated by the line impedance.
Lt/N
Ct/N
Ct/2N
Reflections: Loading at taps should be at least 10 times the characteristic
impedance to minimize reflections due to transmission line effects. The
reflected voltage due to a tap loaded by a resistance, RL, is given by
Ct/2N
Reflection (%) = 1 - (1 / (1 + Zo/2RL))
Figure 1A. Passive Delay Line Schematic Diagram.
In certain applications, mismatches can be used to achieve pulse-shaping
requirements. There are three basic rules relating to reflections:
Design: This LC network may be used to pass either analog or digital
signals whose bandwidth is compatible with the intended range of operation for the delay line. A specific delay and impedance, determine the
required LC values of the network:
Td =
( Lt x Ct )
ZO =
( Lt / Ct )
1) No reflections at either terminal
of a line which is terminated with
its characteristic impedance.
Td = Total Delay ( ns )
Figure 2A.
Lt = Total Line Inductance ( µH )
2) A reflection, equal in amplitude and of same polarity to the impinging
signal, will occur at the input of a line which is open circuited.
( Rt = infinite, see figures below.)
Ct = Total Line Capacitance ( pF )
tr =
PW > 2xTd
Open: Rt =
PW < Td
tr o2 - tr i2
2xTd
.35 / tr
N
3) A reflection, equal in amplitude and of opposite polarity to the
impinging signal, will occur at the input of a line which is short
circuited. ( Rt = 0, see figures below.)
PW > 2xTd
Short: Rt = 0
PW < Td
(Td / tr)1.36
Attenuation: The output voltage attenuation of a delay line has several
contributing factors:
2xTd
2xTd
2xTd
Figure 4A.
Internal D.C. resistance (DCR)
Dielectric and ground plane losses
Impedance mismatches at terminations
Frequency limitations (BW) of delay line
Circuit Considerations: To assure delay accuracy and prevent signal
distortion, care should be taken to properly integrate the passive delay line
into the circuit design. A board trace can load a tap with several picofarads
of capacitance which will increase delay, rise time, distortion and attenuation. The designer should calculate inductance and capacitance values of
the delay line ( Lt , Ct ) to determine if anticipated board loading is
significant. For typical passive delay line applications, the following design
criteria provide optimum performance:
When the delay line is minimally loaded, properly terminated and the input
pulse widths are significantly greater than the line's rise time, attenuation
is given by:
1.
2.
3.
4.
5.
Attenuation (%) = 1 - (Zo / (Zo + DCR))
Series Connection:
Passive delay lines of the same impedance can be
connected input-to-output (cascaded) to optimize rise time and/or obtain
specific delay values. Termination is required only at the output of the final
stage. The rise time of the grouped lines is given by
tro =
2xTd
Figure 3A.
An analog delay line's bandwidth (-3dB attenuation) is related to the
network's rise time which is dependent upon the total number (N) of LC
sections. The delay-to-rise time ratio is the figure of merit, or Quality Factor,
used to characterize delay lines. Generally, the greater figure of merit
implies higher number of sections, and therefore higher cost. The bandwidth for the network, and number of sections follow these approximations:
1.
2.
3.
4.
5.
Rt
ZO = Impedance ( Ohms )
Rise Time: The rise time of a delay line is typically measured from the 10%
to 90% points of the leading edge of the output pulse. The measured output
risetime ( tr o ) is a function of the input rise time ( tr i ) and the true rise time
of the delay line ( tr ):
BW
Rt = Zo
The line should be properly terminated.
Minimize trace lengths to delay line.
Circuit should have massive ground plane.
All common connections should be used.
We encourage you to call and discuss the details of your design with one
of our application engineers. We offer quick turnaround on samples, and
custom versions are available, generally at no cost for existing package
configurations.
tr i2 + tr 12 + tr 22 + ... tr N2
APP1_PAS 1/98
Rhombus
Industries Inc.
2
15801 Chemical Lane, Huntington Beach, CA 92649-1595
Tel: (714) 898-0960 • Fax: (714) 896-0971
TEST
PROBE
TEST
PROBE
PULSE
GENERATOR
R1
Rg
IN
HIGH BW
(350 MHz min.)
OSCILLOSCOPE
DELAY LINE
UNDER TEST
R2
CH
A
CH
B
TRIG
IN
EXTERNAL
TRIGGER
Rg = GENERATOR SOURCE IMPEDANCE = 50 OHMS
R1, R2 = INPUT MATCHING PAD RESISTORS
Rt = TERMINATING RESISTOR
Zo = DELAY LINES CHARACTERISTIC IMPEDANCE
(Rg 2 x Zo)
(Zo - Rg)
INPUT FALL TIME (Tfi): the elapsed time
between the 90% and the 10% points on the
trailing edge of the input pulse.
Figure 5A. Recommended test circuit for Passive Delay Lines
90%
Pos
INPUT RISE TIME (Tri): the elapsed time
between the 10% and the 90% points on the
leading edge of the input pulse.
90%
INPUT VOLTAGE (Ei): the amplitude of the
input pulse.
At
Ei 50%
Eo
Pw
10%
S
LEADING EDGE: that portion of the pulse
which rises from zero to peak amplitude.
50%
OUTPUT RISE TIME (Tfo): the elapsed
time between the 10% and the 90% points
on the leading edge of the output pulse.
10%
Tri
Tfi
Tro
OUTPUT FALL TIME (Tfo): the elapsed
time between the 90% and the 10% points
on the trailing edge of the output pulse.
Tfo
Td
Figure 6A. Passive Delay Line Waveform Parameters
OUTPUT VOLTAGE (Eo): the amplitude of
the output pulse.
PULSE DISTORTION (S): the magnitude
of the largest peak amplitude of all spurious
responses in either a positive or negative
direction occurring in the period after the top
of the leading edge of the output pulse and
before two time delays (for flat input pulse
top).
VOH
VTrh
VTrh
Ei
Eo V Td
V Td
Pw
VTrl
VTrl
VOL
Tfi
Tri
Td
Tro
LH
Figure 7A.
Td
Rhombus
Industries Inc.
Tfo
PULSE OVERSHOOT (Pos): the peak
amplitude of overshoot occurring at the top
of the leading edge of the output pulse (for
flat input pulse top).
PULSE WIDTH (Pw): the elapsed time
between the 50% points on the leading and
trailing edge of a pulse.
HL
TRAILING EDGE: that portion of the pulse
which falls from peak amplitude to zero.
Active Delay Line Waveform Parameters
Specifications subject to change without notice.
DELAY TIME (Td): the elapsed time
between the respective 50% points on the
leading edges of the input and output
pulses.
IMPEDANCE (Zo):
the effective
impedance of the delay line which is equal
to the value of the terminating impedance
which provides a minimum reflection back
to the input of the delay line.
R1 = {Rg x Zo} / R2
R2 =
Attenuation (At): the difference in peak
amplitude between input and output pulses.
D.C. RESISTANCE (DCR): The D.C.
resistance, in ohms, measured between
the input and output of a delay line.
OUT
Rt = Zo
GLOSSARY
For other values & Custom Designs, contact factory.
3
APP1_PAS 1/98
15801 Chemical Lane, Huntington Beach, CA 92649-1595
Tel: (714) 898-0960 • Fax: (714) 896-0971
```